Image display of a tubular structure

ABSTRACT

Described herein is a technology for facilitating visualization of a tubular structure. Digitized image data of the tubular structure is received and processed to determine a centerline. A first transformation operation is performed on a first set of coordinates representing the tubular structure to generate a transformed tubular structure with a straight centerline. A second transformation operation is then performed locally on a second set of coordinates representing at least one fold of the transformed tubular structure to generate a transformed fold, which is perpendicular to the centerline.

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims the benefit of U.S. provisionalapplication No. 61/263,435 filed Nov. 23, 2009, the entire contents ofwhich are herein incorporated by reference.

TECHNICAL FIELD

The present disclosure relates generally to automated orpartially-automated display of image data, and more particularly toimage display of a tubular structure.

BACKGROUND

With the advent of sophisticated medical imaging modalities, such asComputed Tomography (CT), three-dimensional (3-D) volumetric data setscan be reconstructed from a series of two-dimensional (2-D) X-ray slicesof an anatomical structure taken around an axis of rotation. Such 3-Dvolumetric data may be displayed using volume rendering techniques so asto allow a physician to view any point inside the anatomical structure,without the need to insert an instrument inside the patient's body.

One exemplary use of medical imaging is in the area of preventivemedicine. For example, CT colonography (also known as virtualcolonoscopy) is a valuable tool for early detection of colonic polypsthat may later develop into colon cancer (or colorectal cancer). Studieshave shown that early detection and removal of precursor polypseffectively prevent colon cancer. CT colonography uses CT scanning toobtain volume image data that represents the interior view of the colon(or large intestine). It is minimally invasive and more comfortable forpatients than traditional optical colonoscopy. From CT imageacquisitions of the patient's abdomen, the radiologist can inspect anysuspicious polyps attached to the colon wail by examiningreconstructions of individual planes of the image data or performing avirtual fly-through of the interior of the colon from the rectum to thececum, thereby simulating a manual optical colonoscopy.

Both two-dimensional (2-D) and three-dimensional (3-D) views are oftenprovided in CT colonography. 2-D views are typically cross-sectionalrepresentations of intensities occurring at a given slice. These 2-Dimages may be presented in the axial, coronal and sagittal planes. 3-Dviews present images with a volumetric appearance, similar to an opticalcolonoscopy. Although 3-D views allow the user to examine and detect anybumps on the colon walls, it is often very difficult to differentiatebetween true polyps and irrelevant structures such as residual stools orlipomas. 2-D views, on the other hand, provide the voxel intensitiesnecessary to discriminate between these structures.

The problem with 2-D views, however, is that polyps behind or on thehaustral folds are often missed because the haustral folds change theirshapes drastically according to which cross sections are viewed. In manycases, polyps are dismissed as irrelevant when several cross-sectionalimages are examined, because the folds quickly move away when the slicesto be viewed are changed. As a result, inspecting each fold is extremelytime-consuming, and polyps occurring on the folds are very difficult todetect. Accordingly, the accuracy and sensitivity of computer-aideddiagnosis and treatment of colon cancer are severely impaired by theseshortcomings of conventional systems.

SUMMARY

A technology for facilitating visualization of a tubular structure isdescribed herein. In one implementation, digitized image data of thetubular structure is received and processed to determine a centerline. Afirst transformation operation is performed on a first set ofcoordinates representing the tubular structure to generate a transformedtubular structure with a straight centerline. A second transformationoperation is then performed locally on a second set of coordinatesrepresenting at least one fold of the transformed tubular structure togenerate a transformed fold, which is perpendicular to the centerline.

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the followingdetailed description. It is not intended to identify features oressential features of the claimed subject matter, nor is it intendedthat it be used to limit the scope of the claimed subject matter.Furthermore, the claimed subject matter is not limited toimplementations that solve any or all disadvantages noted in any part ofthis disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the present disclosure and many of theattendant aspects thereof will be readily obtained as the same becomesbetter understood by reference to the following detailed descriptionwhen considered in connection with the accompanying drawings.Furthermore, it should be noted that the same numbers are usedthroughout the drawings to reference like elements and features.

FIG. 1 shows an exemplary system;

FIG. 2 shows an exemplary method;

FIGS. 3 a-c show an exemplary tubular structure during various stages oftransformation;

FIGS. 4 a-b illustrate the local transformation of an exemplary fold;

FIG. 5 a shows a perspective view of an exemplary slice plane;

FIG. 5 b shows an exemplary cross-sectional image;

FIG. 6 shows an example of a cross-sectional image of a portion of acolon; and

FIG. 7 shows an image of a periphery region associated with an exemplarytransformed fold.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forthsuch as examples of specific components, devices, methods, etc., inorder to provide a thorough understanding of embodiments of the presentinvention. It will be apparent, however, to one skilled in the art thatthese specific details need not be employed to practice embodiments ofthe present invention. In other instances, well-known materials ormethods have not been described in detail in order to avoidunnecessarily obscuring embodiments of the present invention. While theinvention is susceptible to various modifications and alternative forms,specific embodiments thereof are shown by way of example in the drawingsand will herein be described in detail. It should be understood,however, that there is no intent to limit the invention to theparticular forms disclosed, but on the contrary, the invention is tocover all modifications, equivalents, and alternatives falling withinthe spirit and scope of the invention.

The term “x-ray image” as used herein may mean a visible x-ray image(e.g., displayed on a video screen) or a digital representation of anx-ray image (e.g., a file corresponding to the pixel output of an x-raydetector). The term “in-treatment x-ray image” as used herein may referto images captured at any point in time during a treatment deliveryphase of a radiosurgery or radiotherapy procedure, which may includetimes when the radiation source is either on or off. From time to time,for convenience of description, CT imaging data may be used herein as anexemplary imaging modality. It will be appreciated, however, that datafrom any type of imaging modality including but not limited to X-Rayradiographs, MRI, CT, PET (positron emission tomography), PET-CT, SPECT,SPECT-CT, MR-PET, 3-D ultrasound images or the like may also be used invarious embodiments of the invention.

Unless stated otherwise as apparent from the following discussion, itwill be appreciated that terms such as “segmenting,” “generating,”“registering,” “determining,” “aligning,” “positioning,” “processing,”“computing,” “selecting,” “estimating,” “detecting,” “tracking” or thelike may refer to the actions and processes of a computer system, orsimilar electronic computing device, that manipulate and transform datarepresented as physical (e.g., electronic) quantities within thecomputer system's registers and memories into other data similarlyrepresented as physical quantities within the computer system's memoriesor registers or other such information storage, transmission or displaydevices. Embodiments of the methods described herein may be implementedusing computer software. If written in a programming language conformingto a recognized standard, sequences of instructions designed toimplement the methods can be compiled for execution on a variety ofhardware platforms and for interface to a variety of operating systems.In addition, embodiments of the present invention are not described withreference to any particular programming language. It will be appreciatedthat a variety of programming languages may be used to implementembodiments of the present invention.

As used herein, the term “image” refers to multi-dimensional datacomposed of discrete image elements (e.g., pixels for 2-D images andvoxels for 3-D images). The image may be, for example, a medical imageof a subject collected by computer tomography, magnetic resonanceimaging, ultrasound, or any other medical imaging system known to one ofskill in the art. The image may also be provided from non-medicalcontexts, such as, for example, remote sensing systems, electronmicroscopy, etc. Although an image can be thought of as a function fromR³ to R or R⁷, the methods of the inventions are not limited to suchimages, and can be applied to images of any dimension, e.g., a 2-Dpicture or a 3-D volume. For a 2- or 3-dimensional image, the domain ofthe image is typically a 2- or 3-dimensional rectangular array, whereineach pixel or voxel can be addressed with reference to a set of 2 or 3mutually orthogonal axes. The terms “digital” and “digitized” as usedherein will refer to images or volumes, as appropriate, in a digital ordigitized format acquired via a digital acquisition system or viaconversion from an analog image.

The following description sets forth one or more implementations ofsystems and methods that facilitate visualization of image data. Oneimplementation of the present framework reconstructs a cross-sectionalimage of a tubular structure (e.g., colon). First, a volume of imagedata containing the tubular structure may be deformed (or transformed)so that the centerline of the tubular structure is straightened. Second,sub-volumes containing folds of the tubular structure may each belocally deformed so that the folds are perpendicular to the centerline.The deformed tubular structure may be rotated about a longitudinal axisof a cylinder virtually disposed around the tubular structure. Thepresent framework finds application in, for example, virtual colonoscopyusing image data of the colon. In the cross-sectional view, polypslocated on the wall of the colon, and particularly, on or behind thehaustral fold, can be readily discovered.

It is understood that while a particular application directed to virtualcolonoscopy is shown, the technology is not limited to the specificembodiment illustrated. The present technology has application to, forexample, visualizing features in other types of luminal, hollow ortubular anatomical structures (e.g., airway, urinary gall bladder, bloodvessel, trachea, intestine, etc.) or non-anatomical objects (e.g., fuelinjection systems). In addition, the present technology has applicationto both medical applications and non-medical applications, such asgeological surveying, manufacturing, and other engineering applications.

FIG. 1 is a block diagram illustrating an exemplary visualization system100. The visualization system 100 includes a computer system 101 forimplementing the framework as described herein. The computer system 101may be further connected to an imaging device 102 and a workstation 103,over a wired or wireless network. The imaging device 102 may be aradiology scanner such as a magnetic resonance (MR) scanner or a CTscanner.

Computer system 101 may be a desktop personal computer, a portablelaptop computer, another portable device, a mini-computer, a mainframecomputer, a server, a storage system, a dedicated digital appliance, oranother device having a storage sub-system configured to store acollection of digital data items. In one implementation, computer system101 comprises a processor or central processing unit (CPU) 104 coupledto one or more non-transitory computer-readable media 106 (e.g.,computer storage or memory), display device 108 (e.g., monitor) andvarious input devices 110 (e.g., mouse or keyboard) via an input-outputinterface 121. Computer system 101 may further include support circuitssuch as a cache, power supply, clock circuits and a communications bus.Even further, computer system 101 may be provided with a graphicscontroller chip, such as a graphics processing unit (GPU) that supportshigh performance graphics functions.

It is to be understood that the present technology may be implemented invarious forms of hardware, software, firmware, special purposeprocessors, or a combination thereof. In one implementation, thetechniques described herein are implemented by image reconstruction unit107. Image reconstruction unit 107 may include computer-readable programcode tangibly embodied in non-transitory computer-readable media 106.Non-transitory computer-readable media 106 may include random accessmemory (RAM), read only memory (ROM), magnetic floppy disk, flashmemory, and other types of memories, or a combination thereof. Thecomputer-readable program code is executed by CPU 104 to process images(e.g., MR or CT images) from imaging device 102 (e.g., MR or CTscanner). As such, the computer system 101 is a general-purpose computersystem that becomes a specific purpose computer system when executingthe computer readable program code. The computer-readable program codeis not intended to be limited to any particular programming language andimplementation thereof. It will be appreciated that a variety ofprogramming languages and coding thereof may be used to implement theteachings of the disclosure contained herein.

In one implementation, computer system 101 also includes an operatingsystem and microinstruction code. The various techniques describedherein may be implemented either as part of the microinstruction code oras part of an application program or software product, or a combinationthereof, which is executed via the operating system. Various otherperipheral devices, such as additional data storage devices, andprinting devices, may be connected to the computer system 101.

The workstation 103 may include a computer and appropriate peripherals,such as a keyboard and display, and can be operated in conjunction withthe entire system 100. For example, the workstation 103 may communicatewith the imaging device 102 so that the image data collected by theimaging device 102 can be rendered at the workstation 103 and viewed onthe display. The workstation 103 may include a user interface thatallows the radiologist or any other skilled user (e.g., physician,technician, operator, scientist, etc.), to manipulate the image data.For example, the user may identify regions of interest in the imagedata, or annotate the regions of interest using pre-defined descriptorsvia the user-interface. Further, the workstation 103 may communicatedirectly with computer system 101 to display processed image data. Forexample, a radiologist can interactively manipulate the displayedrepresentation of the processed image data and view it from variousviewpoints and in various reading modes.

FIG. 2 shows an exemplary method 200 of displaying a cross-sectionalview of a tubular structure. The exemplary method 200 may be implementedby the image reconstruction unit 107 in computer system 101, previouslydescribed with reference to FIG. 1. FIGS. 3-5 illustrate an exemplarytubular structure during various stages of transformation in accordancewith the method 200.

At step 202, the computer system 101 receives image data of a tubularstructure. The image data includes one or more digitized images acquiredby, for example, imaging device 102. The imaging device 102 may acquirethe images by techniques that include, but are not limited to, magneticresonance (MR) imaging, computed tomography (CT), helical CT, x-ray,positron emission tomography, fluoroscopic, ultrasound or single photonemission computed tomography (SPECT). The images may include one or moreintensity values that indicate certain material properties. For example,CT images include intensity values indicating radiodensity measured inHounsfield Units (HU). Other types of material properties may also beassociated with the intensity values. The images may be binary (e.g.,black and white) or grayscale. In addition, the images may comprise twodimensions, three dimensions, four dimensions or any other number ofdimensions. The tubular structure may be any lumen-defining structure,such as a colon, blood vessel, bladder, trachea, intestine or any otheranatomical structure. In addition, the tubular structure may also be anon-anatomical structure.

At 204, the image data is pre-processed, either automatically by thecomputer system 101, manually by a skilled user (e.g., radiologist), ora combination thereof. Various types of pre-processing may be performed.For example, the images may be pre-filtered to remove noise artifacts orto enhance the quality of the images for ease of evaluation. Other typesof filtering or pre-processing may also be performed.

In one implementation, pre-processing includes segmenting the image datainto a region of interest (ROI). An ROI is an area or volume identifiedfor further study and examination. Such ROI may represent at least aportion of a tubular structure (e.g., colon). The ROT may beautomatically detected by the computer system 101 using a computer-aideddetection (CAD) technique, such as one that detects points where thechange in intensity exceeds a certain threshold. Alternatively, the ROImay be identified by a skilled user via, for example, a user-interfaceat the workstation 103. The ROIs may also be tagged, annotated or markedfor emphasis or to provide additional textual information so as tofacilitate interpretation.

In addition, the pre-processing may also include detecting oridentifying folds associated with the tubular structure. In the contextof virtual colonoscopy, for example, haustral folds may be detected.Folds may be detected by a region growing process. In oneimplementation, seed points for region growing may be identified on thesurface of the structure where curvature characteristics correspond to ahyperbolic curve. An exemplary region growing process is described inU.S. patent application Ser. No. 12/879,038, filed on Sep. 10, 2010,which is hereby incorporated by reference. Other methods may also beused to detect the folds.

At 206, the image reconstruction unit 107 determines a centerline of atubular structure 302 detected in the image data. FIG. 3 a illustratesan exemplary 3-D tubular structure 302 with a centerline 304. Thecenterline 304 may be represented by a skeleton or a medial axis. In oneimplementation, the centerline 304 is defined as a thin representationthat is equidistant from at least two or three voxels on the structure'sboundary surface (or inner wall surface). Alternatively, the centerlinemay be defined as the locus of the centers of maximal spheres containedin the structure 302.

Various techniques may be employed to compute the centerline 304. Forexample, skeletonization methods, such as distance transform,morphological thinning, path planning, flux-driven methods, extractionfrom level sets, and so forth, may be applied. See, for example, thefollowing patents, which are hereby incorporated by reference: U.S. Pat.No. 7,081,088 entitled “Method and apparatus for automatic local pathplanning for virtual colonoscopy”; U.S. Pat. No. 7,457,444 entitled“Method and apparatus for fast automatic centerline extraction forvirtual endoscopy”; and U.S. Pat. No. 7,300,398 entitled “Method andapparatus for registration of virtual endoscopic images.”

Referring back to FIG. 2, at 208, the image reconstruction unit 107performs a first transformation (or deformation) operation on a firstset of coordinates representing the tubular structure 302. A transformedtubular structure 302 with a straight centerline 304 is generated as aresult. This straightening step unfolds the tubular structure 302 into alongitudinal structure, which may be approximated by a hypotheticalbounding cylinder. For purposes of illustration, FIGS. 3 a and 3 b showthe tubular structure 302 before and after the first transformationrespectively. As shown, a hypothetical cylinder 306 may be virtuallydisposed around the tubular structure 302. In one implementation, thehypothetical cylinder 306 has a constant radius and an associated globalcoordinate system. In one implementation, the global coordinate systemcomprises a Cartesian coordinate system defined by orthogonal X, Y and Zaxes. The centerline 304 of the tubular structure 302 may serve as thelongitudinal Y-axis of the hypothetical cylinder 306. It is understoodthat other types of coordinate systems may also be used.

The straightening of the centerline 304 may be achieved by performing aseries of one or more affine transformation operations on the first setof coordinates associated with the tubular structure 302. An affinetransformation is a geometric transformation that preserves theco-linearity between points and the ratios of distances along a line. Anaffine transformation may include a linear transformation (e.g.,rotation, scaling, shear) and a translation (or shift). The affinetransformation may be performed on sub-volumes along the centerline. Theparameters of the affine transformation may be determined so that thecenterline 304 becomes a straight line. It is understood that variousother techniques, such as uniform sampling, conformal mapping, distancetransform, mesh skinning or skeletal subspace deformation, may beemployed to straighten the centerline 304. See, for example, U.S. patentapplication Ser. No. 12/398,220, filed on Mar. 5, 2009, which is herebyincorporated by reference.

Referring to FIG. 2, at 210, the image reconstruction unit 107 performssecond transformation operation locally on a second set of coordinates.The second set of coordinates represents a fold of the transformedtubular structure 302. The transformation generates a transformed foldthat is perpendicular to the centerline 304. FIGS. 3 b-c show thetubular structure 302 before and after such local transformationrespectively. As shown, each fold segment 308 may be localized in asub-volume 309 (depicted by hatched lines). The sub-volume 309 may be apre-determined sub-volume, such as a cubic sub-volume (e.g., 20×20×20mm) centered at the centroid of the fold.

The local transformation may be performed on voxels in each sub-volume309, such that the vertical z-axis 310 of the fold 308 becomesperpendicular relative to the longitudinal Y-axis. In addition, theintermediary segments 312 between the folds 308 may be locallytransformed to maintain the natural continuity of the surface of thetubular structure 302. In one implementation, a linear interpolationoperation is performed on the intermediary segments 312. Other types ofinterpolation operations; such as tri-linear or tri-cubic interpolationoperations, may also be performed.

After performing such local transformation operations, the folds 308will be substantially stationary when projected on a longitudinal planerotating about the Y axis, as will be described later. Such featureadvantageously facilitates the detection of inconspicuous polyps assubtle bumps on the folds. Regions behind the folds, which wouldotherwise be occluded in conventional systems, will also be exposed forexamination. This capability is especially useful in, for example,virtual colonoscopy, where polyps are commonly hidden behind thehaustral folds.

FIGS. 4 a and b illustrate the local transformation of the fold 308 infurther detail. In particular, FIGS. 4 a and b show a perspective viewand a cross-sectional view of the fold 308 respectively. Referring toFIG. 4 a, a plane 402 dividing the fold 308 substantially equally intotwo portions may first be determined. The dividing plane 402 may bedetermined by using a least squares method. In one implementation, theleast squares method minimizes the sum of squared distances to the plane402 from a given set of points {d1, d2, d3, . . . , di} disposedthroughout the surface 404 of the fold 308. In other words, the dividingplane 402 may be defined by one or more points that best fit the set ofpoints {d1, d2, d3, . . . , di} on the fold surface 404. Such best fitpoints are determined by optimizing the minimum sum

$S = {\left( {\sum\limits_{i = 1}^{n}d_{i}^{2}} \right).}$The optimization may be performed by, for example, solving a matrixeigenvalue problem. Other methods of computing the dividing plane 402are also useful.

The fold 308 may be associated with a local coordinate system. In oneimplementation, the local coordinate system comprises a Cartesiancoordinate system with origin O and orthogonal x-, y- and z-axes. Theorigin O of the local coordinate system may be arbitrarily selected.Alternatively, the centroid of the points on the fold surface 404 (asdepicted in FIG. 4 a) may serve as the origin O. In addition, the normalvector of the dividing plane 402 may serve as the x-axis, and twoperpendicular vectors lying on the dividing plane 402 may serve as they- and z-axes. One way of determining the y-axis is to compute a linethat minimizes the squared distances from each point on the fold surface404 to the line. It is understood that other types of coordinate systemsmay also be used.

After the dividing plane 402 is defined, a series of one or more localtransformations may then be applied to the coordinates of the fold 308so as to align the local z-axis with the global Z-axis of thehypothetical cylinder 306. As shown in FIG. 4 b, the fold structure 308may be rotated by an angle A about the local x-axis. The series of localtransformations include, for example, one or more affinetransformations. The z-axis 310 of the transformed fold 308 will beperpendicular to the longitudinal Y-axis 304 of the hypotheticalcylinder 306, as illustrated by FIG. 3 c.

Referring back to FIG. 2, at 212, a longitudinal cross-sectional imageof the tubular structure is rendered. The cross-sectional image may begenerated by re-sampling the volumetric image data on a slice planeoriented along the longitudinal axis of the hypothetical cylinder. FIG.5 a shows a perspective view of the slice plane 506. As shown, the sliceplane 506 passes through the global longitudinal Y-axis (or centerline304). The slice plane 506 may be rotated about the global Y-axis tochange the resulting cross-sectional image 509 viewed on the displaydevice. In one implementation, the rotation is performed in response touser commands. The user commands may be received by the computer system101 from, for example, an observer at a workstation 103 with acorresponding user interface (e.g., mouse, keyboard, graphical userinterface).

FIG. 5 b shows the corresponding cross-sectional slice image 509 outputby, for example, computer system 101. As shown, the cross-sectionalslice image 509 includes a representation 510 of the tubular structure302 with folds 308 that are perpendicular to the longitudinal axis 304.The representation 510 may be a three-dimensional (3-D) surfacerendering of the tubular structure 302. The 3-D representation providesuseful geometric information (e.g., width, depth, height) about thetubular structure 302. In addition, a two-dimensional (2-D)representation of the periphery region 512 of the tubular structure maybe displayed. The intensity (or brightness) of the pixels in the 2-Drepresentation may provide indications of the material properties (e.g.,densities) of the tissues on or surrounding the tubular structure 302.The pixels in the 2-D representation may also be color-coded inaccordance with a transfer function to facilitate differentiationbetween the different types of tissue.

The slice image 509 may be generated by performing one or more volumerendering techniques, volume ray casting, ray tracing, splatting, shearwarping, texture mapping, or a combination thereof. For example, a raymay be projected from a viewpoint for each pixel in the frame bufferinto a volume reconstructed from the image data. As the ray is cast, ittraverses through the voxels along its path and accumulates visualproperties (e.g., color, transparency) based on the transfer functionand the effect of the light sources in the scene. The slice image 509 isrendered for display on, for example, output display device 108. Inaddition, the rendered image 509 may be stored in a raw binary format,such as the Digital Imaging and Communications in Medicine (DICOM) orany other file format suitable for reading and rendering image data fordisplay and visualization purposes.

FIG. 6 shows an example of a cross-sectional image 600 of a portion of acolon that can be reconstructed using the method 200. As shown, thecross-sectional image 600 comprises a 3-D representation 602 of aportion of a colon along the longitudinal axis. Unlike conventionalfillet views, haustral folds 604 are easily seen. In this view, haustralfolds 604 are locally perpendicular to the longitudinal axis, such thatthe folds 604 are substantially stationary when the slices to be viewedare changed or rotated about the longitudinal axis. An advantage of thiscross-sectional view is that significantly large portions of thehaustral folds can be viewed in a single image. Accordingly, any polypslocated on or behind the folds can easily be detected.

FIG. 7 shows another image 702 which magnifies a periphery regionassociated with exemplary transformed vertical fold. As shown, voxelintensities within the periphery region 704 of the vertical fold arevisible, thereby facilitating the discrimination between polyps andirrelevant structures (e.g., lipomas or residual stool). In addition,any polyps located on or behind the fold can easily be detected byexamining the voxel intensities. These features greatly enhance theaccuracy and sensitivity of computer-aided detection of cancer.

Although the one or more above-described implementations have beendescribed in language specific to structural features and/ormethodological steps, it is to be understood that other implementationsmay be practiced without the specific features or steps described.Rather, the specific features and steps are disclosed as preferred formsof one or more implementations.

The invention claimed is:
 1. A method performed by a computer system forvisualizing a tubular structure, comprising: (i) receiving digitizedimage data of the tubular structure; (ii) determining a centerline ofthe tubular structure; (iii) performing a first transformation operationon a first set of coordinates representing the tubular structure togenerate a transformed tubular structure with a straight centerline;(iv) defining a local axis of a fold of the transformed tubularstructure, wherein the local axis lies on a dividing plane that dividesthe fold substantially equally into two portions; and (v) performing asecond transformation operation locally on a second set of coordinatesrepresenting the fold of the transformed tubular structure to generate atransformed fold, wherein the local axis of the transformed fold isperpendicular to the centerline.
 2. The method of claim 1 furthercomprising: acquiring, by an imaging device, the image data by computedtomography (CT).
 3. The method of claim 1 wherein the tubular structurecomprises a colon.
 4. The method of claim 1 further comprising:segmenting the image data into a region of interest, wherein the regionof interest represents at least a portion of the tubular structure. 5.The method of claim 4 further comprising detecting the at least one foldby a region growing process.
 6. The method of claim 1 wherein the firsttransformation operation comprises an affine transformation operation.7. The method of claim 1 further comprising performing an interpolationoperation on segment coordinates representing a segment between twofolds of the tubular structure.
 8. The method of claim 1 wherein thelocal axis defines a local Cartesian coordinate system.
 9. The method ofclaim 1 wherein the defining the local axis comprises determining thedividing plane by performing a least squares method.
 10. The method ofclaim 1 wherein the second transformation operation comprises one ormore affine transformation operations.
 11. The method of claim 10wherein the one or more affine transformation operations comprise atleast one rotation operation.
 12. The method of claim 1 furthercomprising rendering a longitudinal cross-sectional image of thetransformed tubular structure with the transformed fold.
 13. The methodof claim 12 wherein the rendering comprises displaying voxel intensitiesassociated with a periphery region of the transformed tubular structurewith the transformed fold.
 14. The method of claim 13 wherein therendering comprises generating a three-dimensional surface rendering ofthe transformed tubular structure with the transformed fold.
 15. Themethod of claim 12 wherein the rendering comprises generating athree-dimensional surface rendering of the transformed tubular structurewith the transformed fold.
 16. The method of claim 12 wherein therendering comprises: receiving a user command; rotating a slice planeabout the centerline in response to the user command; and re-samplingthe image data on the slice plane to generate the longitudinalcross-sectional image.
 17. The method of claim 16 wherein the renderingfurther comprises generating a three-dimensional surface rendering ofthe transformed tubular structure with the transformed fold.
 18. Themethod of claim 17 wherein the rendering further comprises displayingvoxel intensities associated with a periphery region of the tubularstructure with the transformed fold.
 19. A non-transitory computerreadable medium embodying a program of instructions executable bymachine to perform steps for visualization, the steps comprising: (i)receiving digitized image data of a tubular structure; (ii) determininga centerline of the tubular structure; (iii) performing a firsttransformation operation on a first set of coordinates representing thetubular structure to generate a transformed tubular structure with astraight centerline; (iv) defining a local axis of a fold of thetransformed tubular structure, wherein the local axis lies on a dividingplane that divides the fold substantially equally into two portions; and(v) performing a second transformation operation locally on a second setof coordinates representing the fold of the transformed tubularstructure to generate a transformed fold, wherein the local axis of thetransformed fold is perpendicular to the centerline.
 20. A visualizationsystem, comprising: a memory device for storing computer readableprogram code; and a processor in communication with the memory device,the processor being operative with the computer readable program codeto: (i) receive digitized image data of a tubular structure; (ii)determine a centerline of the tubular structure; (iii) perform a firsttransformation operation on a first set of coordinates representing thetubular structure to generate a transformed tubular structure with astraight centerline; (iv) define a local axis of a fold of thetransformed tubular structure, wherein the local axis lies on a dividingplane that divides the fold substantially equally into two portions; and(v) perform a second transformation operation locally on a second set ofcoordinates representing the fold of the transformed tubular structureto generate a transformed fold, wherein the local axis of thetransformed fold is perpendicular to the centerline.